I think you should remove assigning value to seed in your model.
persistent rngInit;
if isempty(rngInit)
%seed = 2346;
rng(seed)
rngInit=true;
end
% Exponential inter-arrival time dt
mean = 1/10;
dt = -mean*log(1-rand());
and set the value of seed in base workspace using your gui callback.
function seed_Callback(hObject, eventdata, handles)
% hObject handle to seed (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of seed as text
% str2double(get(hObject,'String')) returns contents of seed as a double
value=get(handles.seed,'string');
string1=value{1};
load_system('modelloPerProve');
evalin('base','seed = 1234')
